Chasing a target of 166 for a win, Boucher joined his South African teammate Jacques Kallis with the Bangalore Royal Challengers in a bit of a spot at 106 for four in the 14th over. However the two South Africans put on 55 runs in just 5.1 overs to tilt the scales of the match in the visitors favour. Mark Boucher (39 not out) was the highest scorer for the Bangalore team while captain Rahul Dravid (32), Jacques Kallis (25) and Virat Kohli (23) also chipped in with useful contributions.
Stand-in captain Harbhajan Singh was the pick of the Mumbai bowlers with a couple of wickets to his name.
Earlier, a late assault by Shaun Pollock helped Mumbai Indians reach a competitive 165 for six.
The retired ace South African all rounder cracked three sixes and two fours in his 12-ball cameo while making 28 after coming in at number seven.
The hosts lost wickets regularly after stand-in captain Harbhajan Singh opted to bat first on winning the toss and their total was built mainly around opener Sanath Jayasuriya (29), top-scorer Robin Uthappa (48) and Pollock.
The home team, in the absence of injured captain Sachin Tendulkar got off to a good beginning after the early fall of Luke Ronchi in the second over with Sanath Jayasuriya showing cracking form as he hit five fours and a six in his 16-ball knock before he was run out.
A brilliant pick-up and direct hit ended Jayasuriya innings, an over after he had creamed 16 runs off Jacques Kallis's first over, with a flurry of three fours and an on-driven six.
Dominic Thornely, who came in at one-down at the fall of Australian compatriot Luke Ronchi (8), receiving a nasty blow on his left eyebrow by a soaring ball from Indian pace spearhead Zaheer Khan as tried to pull and missed connecting completely.
He retired hurt and did not come out to bat again and was taken to hospital, where he is kept under observation.
Uthappa and Pinal Shah, the Baroda wicket keeper, joined forces and helped the score past the 70 mark at the halfway stage.
Uthappa, at times beaten by his Karnataka Ranji team-mate Vinay Kumar, also swung the bowler for a six over square leg.
He tried to play the unorthodox scoop shot a number of times and missed quite often before connecting once off Kallis that fetched a boundary.
After being dropped at deep square leg by Vinay off Praveen when on 32, he continued to look for runs.
Uthappa fell, stumped by Mark Boucher, when trying the scoop once too often as the ace South African stumper stood up to B Akhil and took off the bails when the batsman failed to connect.
He struck five fours and a six in his 36-ball knock and also added 28 runs in quick time with Abhishek Nayar.
Nayar hoisted Vinay Kumar for a six and then Pollock struck the medium pacer for a four and a six towards the extra cover region as the bowler went for 20 runs in the 18th over of the innings to boost the run-rate.
Pollock fell off the last ball of the innings to give Zaheer Khan, who was the pick of the attack along with veteran left arm spinner Sunil Joshi, his second wicket.
This was Royal Challengers first win after losing to Kolkata Knight Riders in the opening match, while the Mumbai Indians began their campaign in this league on a losing note.